Project index
Please select from the following areas of research:
Physics 437: theoretical condensed matter physics
Understanding protein folding from polymer models
The current understanding of the characteristics of protein folding is widely based on statistical-physics models of polymers that capture the essential interactions in real protein systems. The reduction of the degrees of freedom of the involved coordinates in such a model, in comparison with the all-atom modelling approach, allows for accumulation of adequate statistics in computer simulations. This type of models has been successfully used to explore the underlying physical mechanism of structural formation, folding dynamics and protein-protein interaction.
Tom P. Devereaux
PHY 258 ext. 6901
Computational approaches to strongly correlated electrons
Surprisingly, there are very few exact results for the simplest model to describe strongly interacting electrons – the Hubbard model. This model is believed to hold an appropriate physical description of high temperature superconductivity. The project involves calculating optical properties of strongly interacting electrons using the "FLEX" approach to the Hubbard model. The primary task is writing code to evaluate integral expressions. Work will be performed in collaboration with experimental groups involved in Raman scattering in Vancouver and Munich.
Raman scattering in new borocarbide superconductors
The discovery of the high temperature superconductors in 1986 has opened the door to the discovery of completely new family of materials with unexpectedly high transition temperatures. Materials involving boron and carbon, called the Borocarbides, have transition temperatures on the order of 25 degrees Kelvin. Currently it is hotly debated whether these materials are more similar to conventional (such as tin) or unconventional (such as the high Tc's) superconductors. Raman scattering experiments have addressed this issue, but have lacked theoretical interpretation of the results. The primary task of this project is writing code to evaluate integral expressions for Raman scattering for Borocarbide systems. Work will be performed in collaboration with the experimental group involved in Raman scattering at the University of Illinois at Urbana-Champaign.
Computer simulations of magnetic vortices in high temperature superconductors: vortex pinning
One of the most vexing problems preventing the widespread use of high temperature superconductors is how to reduce the dissipation caused by applied magnetic fields. The main goal of this project is to try to pin "vortices" of magnetic flux so they cannot move in response to external forces. Computer simulations of these vortices, modeled as flexible strings, driven by applied and internal forces will be carried out using existing molecular dynamics codes. Since our understanding of the motion of extended objects in a dissipative environment is important to our knowledge of properties of polymers, and orientation/folding in proteins, the results may also open new areas of investigation in the area of soft condensed matter physics and biophysics.
Computer simulations of magnetic vortices in high temperature superconductors: commensuration effects
Recent experiments taken on high temperature superconductors have found intriguing evidence for the existence of resistivity minimum as an applied magnetic field is increased such that the number of vortices matches the number of defects, and then again when there are three times as many vortices as defects. Presently there is no theoretical understanding of these results. Once again, this project involves using existing molecular dynamics codes to simulate the motion of vortices in a dissipative environment. Direct comparison with the experimental data is desired.
Computer simulations of molecular biophysics
During the last few years, molecular biophysics has become a very active field of research. The main goal of this project is to investigate the dynamical elastic properties of biopolymers, particularly the DNA molecule, under physical conditions close to that encountered in living organisms. The student will be expected to take existing code and modify it using several different model approaches to molecular biophysics to explore molecular dynamics. Particularly I am interested in determining time scales for macroscopic response to applied forces – knowledge that is needed for molecular engineering and molecular electronic applications.
Michel Gingras
PHY 364 ext. 5697
My main research interests are devoted towards the theoretical study of condensed matter systems such as superconductors, exotic and novel quantum magnets, liquid crystalline systems, etc. I am particularly interested in doing theory that can be tested against real experiments, as opposed to doing "theory in the vacuum" with no direct testability. In this context, an important part of my research efforts makes use of a battery of computational and numerical methods. The 1999 Nobel prize winners Gerard 't Hooft, and Martinus Veltman approached the problem of renormalizability of the electroweak theory of particle physics using the Schoonschip computer program.Clearly, it must be ok for physicists to tackle difficult problems trying to get physical insight using (sometime clever) numerical schemes.
I have interests and research projects available from anyone from third year physics, Masters, Ph.D. and post-doctoral level. Examples of available projects include, but are not limited to:
Monte carlo/molecular dynamics study of the role of applied magnetic field in highly frustrated magnets
Frustration in a condensed matter system occurs when the system cannot minimize its total classical ground state energy by minimizing its pairwise interactions, pair by pair. In the context of magnetic systems, highly frustrated systems are currently attracting much attention by both experimentalists and theorists. So far, little theoretical effort has been devoted to investigate how applied magnetic field influence the behavior of frustrated systems. The aim of this project is to investigate this question and attempt making contact with experiments.
Quantum corrections to the thermodynamic properties of highly frustrated quantum magnets
Quantum fluctuations in condensed matter systems are predominant at ... zero temperature. However, they already manifest themselves at finite (high) temperatures. The aim of this project is to investigate using perturbative approach the role of quantum fluctuations on various condensed matter systems at finite temperature.
Theoretical study of long-range proton order in ice (water)
In common ice water, the oxygen atoms are ordered on a regular crystalline lattice. The hydrogen atoms (protons) are randomly frozen in, giving rise to the famous "Pauling Entropy". The aim of this project is to use a number of the approaches recently developed in the field of frustrated magnetism to explore the problem of frozen-in proton disorder in ice water.
Quantum annealing protocol in ice (water) and spin ice
In some condensed matter system, such as ice water, a macroscopic number of degrees of freedom are often frozen out of equilibrium. Perturbative quantum fluctuations can introduce quantum tunneling "events" and "help" equilibrate the system. The aim of this project is to investigate quantum annealing effects (and protocol) in frozen systems and speed up of relaxation via tunneling events.
Quantum entanglement and concurrence at quantum phase transitions
Strongly correlated electron and spin systems can exhibit phase transitions are zero temperature in a phenomenon called "quantum phase transitions". On the other hand, entanglement is a key feature that describes quantum mechanical systems. The aim of this project is to investigate the behavior of quantum mechanical entanglement in condensed matter models and systems at quantum phase transitions.
Thermodynamic behavior of liquid crystalline materials in confined random geometries
There has recently been much experimental interests devoted to the study of the thermodynamic properties of liquid, solids, liquid crystals, polymers, etc in confined random environment (i.e. water in cement!). Such a problem is of peripheral relevance to understanding the properties of some biologically related materials. Unfortunately, the theoretical treatment of such systems is very difficult and it is not clear what is the physics going on in those systems.
The aim of this project would be to investigate using large scale simulations some simple toy models for the behavior of liquid crystal materials in confined random geometries (i.e. aerogels).
Theoretical study of the quantum antiglass state
In the majority of condensed matter systems, the lower the temperature gets, the slower the internal dynamics of the relevant degrees of freedom.
In a peculiar system, the opposite happens. The lower the temperature, the faster the dynamics. This suggests the "opening" of quantum mechanical tunneling pathways in phase space. There are no existing theories of this problem. The aim of this project is to explore some ideas as to what may cause this "anti" (quantum mechanical) freezing and what are the physically relevant quantum mechanical tunneling channels.
Cluster series expansion study of strongly correlated quantum condensed matter systems
Strongly interacting quantum mechanical systems constitute a formidable problem. There exist various ways to investigate the properties of such systems. The aim of this project is to learn a perturbation method called the "cluster series expansion" method to study the thermodynamic properties of a number of topical problems in the area of strongly correlated electron and spin systems.
Bose condensation in a system of interacting bosons
The purpose of this project is to learn the formalism of Bose condensation of Schwinger bosons in a system of interacting bosons representation of a quantum system with N-body interactions.
Quantum critical phenomenon in a simple model
The aim of this project is to learn a simple (mean) field theory for the problem of a transition at low (and absolute zero) temperature in a simple spin system which is driven by quantum fluctuations as opposed to thermal fluctuations.
Quantum monte carlo simulations
The goal of this project is to learn the technique of quantum simulation techniques to study the thermal and quantum fluctuation properties of interacting quantum bosons and/or fermion systems.
Isotopic mass defect
The purpose of this project is to investigate how isotopic abundance in real materials (and therefore {isotopic} mass defects) alter various thermodynamic properties, and may in the extreme case result in a quantum phase transition driven at zero temperature by quantum fluctuations as opposed to thermal fluctuations.
Effective N-body interactions derived from an interacting quantum N-body system
The goal here is to consider a spin system of interacting quantum spin systems and utilized various form of perturbation techniques to eliminate the high energy sector of the theory and to obtain an effective many-body low-energy theory similar conceptually in the relativistic corrections to Schrodinger's equation when starting from the Dirac equation.
Orientational glasses
Mixed molecular crystals such as N2-Ar, KBr-KCN, ortho-H2/para-H2, display a glass like phase transitions as the system is cooled through its solid phase. The goal of this project is to investigate this problem via numerical simulation techniques using the University of Waterloo-Condensed Matter Theory Beowulf Cluster Hydra.
Potts glasses
Very new results have recently been obtained in the area of phase transitions of spin glasses. While 20 years or so spanning 1980-2003 had led to the belief that there were no phase transitions in these systems, recent large scale simulation studies have changed that view. Potts glasses are intermediate models which sit on the boundary between magnetic spin glasses and "real" (window) molecular glasses. The aim of this project is to use the University of Waterloo-Condensed Matter Theory Beowulf Cluster Hydra to investigate, using advanced simulation techniques, the problem of phase transition in Potts glasses.
Boundary between ice and glass
Much progress has recently been achieve in discovering and explaining a novel class of magnetic systems and models that are the formal statistical mechanics analogue of the Linus Pauling proton disorder problem in ice water -- these systems have been named "spin ices". In ice water, doping with KOH `resolves' the Pauling entropy paradox and give rise to a fully ordered crystalline proton state in ice water. Does the same physics occur in diluted spin ice, or does diluted magnetic spin ice become spin glasses? The aim of this project is to explore this question using large numerical simulations.
Non-universality at a phase transition
Second order phase transitions exhibit the universality (same critical exponents among various famillies of problems). A highly frustrated magnetic material, FeF3, has been found to display "novel/unconventional" critical exponents, hence a "new" universality. There is no current understanding of this paradox. In this project, the student will explore a new idea as to the origin of this using various numerical techniques.
Renormalization group in an "Antiglass"
In most glassy systems, the dynamics slows down continuously as the temperature is reduced. A recently discovered material, LiHoYF4, exhibits the opposite trend. Spin dynamics seems to accelerate upon cooling. Why? Is it due to the formation of macroscopic quantum tunneling events, or other reason. The goal of this project is to learn and use a renormalization technique to investigate a scenario via which a toy model for LiHoYF4 is driven from a glassy state to an antiglass state via divergences of quantum fluctuations in the quantum ground state.
Theory of long-range ionic order in ice water and battery materials
Novel battery (spinel-based) battery material LiMn2O4 share an analogy with the Pauling problem of proton disorder in ice water: the number of zero charged ground states is (naively) infinite, causing a violation of zero entropy at zero temperature, and hence a violation of the Third Law of Thermodynamics. In a related problem, that of spin ice, theorists at the University of Waterloo have been able to resolve that problem/paradox. The aim of this project is to implement the same conceptual approach (although different in details) to the spinel battery materials as well as ice water.
